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Math Help - derivative and tangent line issues

  1. #1
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    derivative and tangent line issues

    Below, there is a problem that I just cannot solve, I've tried all kinds of ways but nothing works. So by getting a large variety of opinions and solutions, I can be able to solve this problem.

    Let f(x) =1/(x-8). Calculate the difference quotient
    {f(6+h)-f(6)}/h for
    h=.1__
    h=.01__
    h=-.01__
    h=-.1__
    If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=6 was -1/n^2 for some integer n what would you expect n to be?
    n=__



    Thanks you in advance
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  2. #2
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    Quote Originally Posted by Skakuntala View Post
    Below, there is a problem that I just cannot solve, I've tried all kinds of ways but nothing works. So by getting a large variety of opinions and solutions, I can be able to solve this problem.

    Let f(x) =1/(x-8). Calculate the difference quotient
    {f(6+h)-f(6)}/h for
    h=.1__
    h=.01__
    h=-.01__
    h=-.1__
    If someone now told you that the derivative (slope of the tangent line to the graph) of f(x) at x=6 was -1/n^2 for some integer n what would you expect n to be?
    n=__



    Thanks you in advance
    This is not good. It is a simple algebra problem. You haven't forgotten your algebra, have you?

    f(x) = 1/(x-8)
    f(6) = 1/(6-8) = 1/(-2) = -1/2
    f(6+h) = 1/(6+h-8) = 1/(h-2)

    Now what?
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